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The No-Show Paradox Under a Restricted Domain

Author

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  • Dan S. Felsenthal

    (University of Haifa)

  • Hannu Nurmi

    (University of Turku)

Abstract

The no-show paradox occurs whenever a group of identically-minded voters is better off abstaining than by voting according to its preferences. Moulin’s (J Econ Theory 45:53–64, 1988) result states that if one wants to exclude the possibility of the no-show paradox, one has to resort to procedures that do not necessarily elect the Condorcet winner when one exists. This paper examines ten Condorcet-consistent and six Condorcet-non-consistent procedures in a restricted domain, viz., one where there exists a Condorcet winner who is elected in the original profile and the profile is subsequently modified by removing a group of voters with identical preferences. The question asked is whether the no-show paradox can occur in these settings. It is found that only two of the ten Condorcet-consistent procedures investigated (Maximin and Schwartz’s procedure) are not vulnerable to the no-show paradox, whereas only two of the six non-Condorcet-consistent ranked procedures investigated (Coombs’ and the Negative Plurality Elimination Rule procedures) are vulnerable to this paradox in the restricted domain. In other words, for a no-show paradox to occur when using Condorcet-consistent procedures it is not, in general, necessary that a top Condorcet cycle exists in the original profile, while for this paradox to occur when using (ranked) non-Condorcet-consistent procedures it is, almost always, necessary that the original profile has a top cycle.

Suggested Citation

  • Dan S. Felsenthal & Hannu Nurmi, 2019. "The No-Show Paradox Under a Restricted Domain," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(4), pages 277-293, April.
    • Handle: RePEc:spr:homoec:v:35:y:2019:i:4:d:10.1007_s41412-018-00079-w
    DOI: 10.1007/s41412-018-00079-w
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    References listed on IDEAS

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    1. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
    2. Dan S. Felsenthal & Hannu Nurmi, 2018. "Voting Procedures for Electing a Single Candidate," SpringerBriefs in Economics, Springer, number 978-3-319-74033-1, October.
    3. Dan S. Felsenthal, 2012. "Review of Paradoxes Afflicting Procedures for Electing a Single Candidate," Studies in Choice and Welfare, in: Dan S. Felsenthal & Moshé Machover (ed.), Electoral Systems, chapter 0, pages 19-91, Springer.
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    7. Dan S. Felsenthal & Hannu Nurmi, 2017. "Monotonicity Failures Afflicting Procedures for Electing a Single Candidate," SpringerBriefs in Economics, Springer, number 978-3-319-51061-3, October.
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    Cited by:

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    2. David McCune & Adam Graham-Squire, 2023. "Monotonicity Anomalies in Scottish Local Government Elections," Papers 2305.17741, arXiv.org, revised Oct 2023.

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    More about this item

    Keywords

    Condorcet-consistency; Domain restrictions; No-show paradox; Voting paradoxes; Voting procedures;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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